@techreport{Duersch2010Pure,
abstract = {It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors game. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure saddle point. Further sufficient conditions for existence are provided. We apply our theory to a rich collection of examples by noting that the class of symmetric two-player zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of a finite population evolutionary stable strategies.},
address = {Heidelberg},
author = {Peter Duersch and J\"{o}rg Oechssler and Burkhard C. Schipper},
copyright = {http://www.econstor.eu/dspace/Nutzungsbedingungen},
doi = {10.11588/heidok.00010545},
keywords = {C72; C73; 330; Symmetric two-player games; zero-sum games; Rock-Paper-Scissors; single-peakedness; quasiconcavity; Nichtkooperatives Spiel; Evolution\"{a}re Spieltheorie; Mathematik; Theorie},
language = {eng},
note = {urn:nbn:de:bsz:16-opus-105453},
number = {500},
publisher = {University of Heidelberg, Department of Economics},
title = {Pure Saddle Points and Symmetric Relative Payoff Games},
type = {Discussion Paper Series},
url = {http://hdl.handle.net/10419/127322},
year = {2010}
}